Match the C p C v ratio for ideal gases with different type of molecules: Molecule Type C p / C v (A) Monoatomic (I) 7 / 5 (B) Diatomic rigid molecules (II) 9 / 7 (C) Diatomic non-rigid molecules (III) 4 / 3 (D) Triatomic rigid molecules (IV) 5 / 3

(A) – (IV), (B) – (I), (C) – (II), (D) – (III)

(A) – (IV), (B) – (II), (C) – (I), (D) – (III)

(A) – (III), (B) – (IV), (C) – (II), (D) – (I)

(A) – (II), (B) – (III), (C) – (I), (D) – (IV)

EASY

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The average kinetic energy of a monatomic molecule is $0.414 eV$ at temperature :

(Use $K_{B} = 1.38 \times 10^{- 23} J {mol}^{- 1} K^{- 1}$ )

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Important Questions on Kinetic Theory of Gases

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

The average energy of molecules in a sample of oxygen gas at

300 K

are

6.21 \times 10^{- 21}

J .

The corresponding values at

600 K

are

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

Using equipartition of energy, the specific heat (in $J {kg}^{- 1} K^{- 1}$ ) of Aluminium at high temperature can be estimated to be (atomic weight of Aluminium $= 27$ )

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

A man is climbing up a spiral staircase. His degrees of freedom are

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

The ratio of the specific heats

\frac{C_{P}}{C_{v}} = γ

in terms of degrees of freedom

(n)

is given by:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

Match the $\frac{C_{p}}{C_{v}}$ ratio for ideal gases with different type of molecules:

Molecule Type	$C_{p} / C_{v}$
(A) Monoatomic	(I) $7 / 5$
(B) Diatomic rigid molecules	(II) $9 / 7$
(C) Diatomic non-rigid molecules	(III) $4 / 3$
(D) Triatomic rigid molecules	(IV) $5 / 3$

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

Given below are two statements:

Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.

Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.

In the light of the above statements, choose the correct answer from the options given below:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

Pressure of an ideal gas is increased by keeping the temperature constant. The kinetic energy of molecules

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature

T ?

(

k_{B}

is Boltzmann constant)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

Molecules of an ideal gas are known to have three translational degrees of freedom. The gas is maintained at a temperature of

T

. The total internal energy,

U

of a mole of this gas, and the value of

γ = (\frac{C_{p}}{C_{v}})

are given, respectively, by

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

The average thermal energy for a mono-atomic gas is : (

k_{B}

is Boltzmann constant and

T

, absolute temperature)

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

If one mole of the polyatomic gas is having two vibrational modes and

β

is the ratio of molar specific heats for polyatomic gas

(β = \frac{C_{P}}{C_{v}})

then the value of

β

is :

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

Question Image

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

A polyatomic ideal gas has

24

vibrational modes. What is the value of

γ ?

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

Two moles of helium are mixed with n moles of hydrogen. If

\frac{C_{p}}{C_{v}} = \frac{3}{2}

for the mixture then the value of

n

is,

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

Two ideal polyatomic gases at temperatures

T_{1}

and

T_{2}

are mixed so that there is no loss of energy. If

F_{1}

and

F_{2}, m_{1}

and

m_{2}, n_{1}

and

n_{2}

be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature

T ?

HARD

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

The number of molecules in one litre of an ideal gas at

2

atmospheric pressure with mean kinetic energy

2 \times 10^{- 9} J

per molecule is:

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

For a gas the value of

\frac{R}{C_{v}} = 0.4,

so the gas is
(R-Universal gas constant)

MEDIUM

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

A gas mixture consists of

3

moles of oxygen and

5

moles of argon at temperature

T

. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of

R T

) of the mixutre is :

EASY

Physics>Heat and Thermodynamics>Kinetic Theory of Gases>Law of Equipartition of Energy and Specific Heat of Gas

The average kinetic energy of a monoatomic gas molecule kept at temperature

27 ° C

is (Boltzmann constant

k = 1.3 \times 10^{- 23} {JK}^{- 1})

The average kinetic energy of a monatomic molecule is 0.414 eV at temperature : (Use KB=1.38×10-23 J mol-1 K-1)

Important Questions on Kinetic Theory of Gases

Learn and Prepare for any exam you want !

The average kinetic energy of a monatomic molecule is $0.414 eV$ at temperature :

(Use $K_{B} = 1.38 \times 10^{- 23} J {mol}^{- 1} K^{- 1}$ )